Modeling Approach for Estimation of Contact and Friction Behavior of Rolling Elements in Linear Bearings
Matthias Reuss*,, Taku Sakai**, and Atsushi Matsubara***
*Makino Milling Machine Co., Ltd.
4023 Nakatsu, Aikawa-machi, Aiko-gun, Kanagawa 243-0303, Japan
**Kyoto Works, Mitsubishi Electric, Kyoto, Japan
***Department of Micro Engineering, Kyoto University, Kyoto, Japan
The improvement in the positioning accuracy of machine tools necessitates reliable friction models for compensation. Friction and damping are primarily caused by mechanical contacts, and they have a wide influence on the dynamics of machine tools. Particularly in the linear motor driven axis, linear bearings induce majority of the friction; contact is observed between the ball and raceway in linear bearings. Based on the Hertzian contact theory and a tangential force model, a model is developed for the friction behavior during the contact between the ball and raceway. This model determines the stick and slip areas, and the relative velocity at the contact surface. Hence, the calculation of the friction force, its hysteresis characteristics, and the stick and slip portions becomes possible.
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